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Spherical Barycentric Coordinates
[article]
2006
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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We develop spherical barycentric coordinates. ...
Furthermore, spherical barycentric coordinates can be used for all applications where only planar barycentric coordinates were available up to now. ...
It follows that there is a bijection between planar barycentric coordinates and spherical barycentric coordinates. ...
doi:10.2312/sgp/sgp06/081-088
fatcat:52sn3674grd3xn7pbklkn6z4zi
Whitney Forms for Spherical Triangles I: The Euler, Cagnoli, and Tuynman Area Formulas, Barycentric Coordinates, and Construction with the Exterior Calculus
[article]
2014
arXiv
pre-print
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We introduce the three barycentric coordinates of a point within the spherical triangle as area ratios which sum to unity. ...
The barycentric coordinates are the Whitney 0-forms, scalar functions over the domain of the triangle associated with each vertex. ...
The Whitney Forms of a Spherical Triangle Let λ A (X) = S A (X) S , λ B (X) = S B (X) S and λ C (X) = S C (X) S be the barycentric coordinates of the point X interior to or on the boundary of ABC, such ...
arXiv:1404.6592v1
fatcat:4fcgnsauuvaaldis5wbrzlwzly
Fast Normal Vector Compression with Bounded Error
[article]
2007
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
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The second uses fixed-precision barycentric coordinates. For both, we provide fast (de)compression algorithms and a rigorous upper bound on compression error. ...
We discuss the effects of base polyhedra on the error bound and suggest polyhedra derived from spherical coverings. ...
The next two integers represent the u and v barycentric coordinates. Since the barycentric coordinates u, v and w sum to 1, there is no need to explicitly store w. ...
doi:10.2312/sgp/sgp07/263-272
fatcat:4t6rlgrebzaifk7cx2w5rw2gku
Generating N-point spherical configurations with low mesh ratios using spherical area coordinates
[article]
2021
arXiv
pre-print
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The method extends Caspar-Klug icosahedral point-grids to non-icosahedral nets through the use of planar barycentric coordinates, which are subsequently interpreted as spherical area coordinates for spherical ...
This short contribution presents a method for generating N-point spherical configurations with low mesh ratios. ...
Homogenizing with spherical area coordinates In order to improve the uniformity of the generated point sets, we can reinterpret the planar barycentric coordinates as a form of spherical barycentric coordinates ...
arXiv:2107.11265v1
fatcat:b6ulwmwrsjdfvnsh7f27s524qa
Deuteron States Model
2018
Journal of Lasers Optics & Photonics
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Barycentrical coordinates are generated to determine a nucleons barycentre [2] . 3. ...
It is postulated that the weak and the spherical, barycentrical coordinates of the strong nucleon interaction are in special relativistic motion towards one another. 5. ...
Barycentrical coordinates are generated to determine a nucleons barycentre [2] . 3. ...
doi:10.4172/2469-410x.1000172
fatcat:csslisgyn5hbtle3l3vzjyuy7i
Mean value coordinates in 3D
2005
Computer Aided Geometric Design
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Trivariate barycentric coordinates can be used both to express a point inside a tetrahedron as a convex combination of the four vertices and to linearly interpolate data given at the vertices. ...
These coordinates generalize in a natural way a recently constructed set of coordinates for planar polygons, called mean value coordinates. ...
Clearly, for any p ∈T , we can express the vector e = p − v as e = τ i (e)e i + τ j (e)e j + τ k (e)e k , where τ i , τ j , τ k are the spherical barycentric coordinates of e. ...
doi:10.1016/j.cagd.2005.06.004
fatcat:ilqtnl7yrfh6picbhr2fgizavu
Temporally-smooth Antialiasing and Lens Distortion with Rasterization Map
[article]
2020
arXiv
pre-print
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To correct barycentric vector, rst distance pass ⃗ is obtained using inverse of the dot-product between spherical-barycentric coordinate ⃗ and the inversed vertex-distance vector. ...
Spherical-barycentric vector ⃗ requires perspective-correction to be used as vertex-data interpolation weight. ...
coordinates . xy , p o l y g [ 1 ] . xy ) , p o l y g [ 2 ] . xy ) −0.5 , 40 max ( max ( p o l y g [ 0 ] . xy , p o l y g [ 1 ] . xy ) , p o l y g [ 2 ] . xy ) +0.5 ) ; 41 } 42 / / Rasterize triangle ...
arXiv:2010.04077v2
fatcat:lh6vkc3xqvcndbozatlezp2o2m
Interpolation on spherical geodesic grids: A comparative study
2007
Journal of Computational and Applied Mathematics
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Most operational models in atmospheric physics, meteorology and climatology nowadays adopt spherical geodesic grids and require "ad hoc" developed interpolation procedures. ...
(a) In [1] spherical barycentric coordinates (b 1 , b 2 , b 3 ) of a point P are introduced as the trihedral coordinates of its position vector v with respect to the trihedron generated by the position ...
(d) In [15] the weights for the bilinear interpolation are the barycentric coordinates evaluated in a local longitude-latitude coordinate system ( , ): if a point P ( , ) belongs to the spherical triangle ...
doi:10.1016/j.cam.2006.10.068
fatcat:lhfmqjuu3jcahc3nw2e2zoff5i
Inverse spherical surfaces
2005
Journal of Computational and Applied Mathematics
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These surfaces can be seen as single-valued functions in spherical coordinates. ...
In this paper we describe a new way to design rational parametric surfaces defined on spherical triangles which are useful for modelling in a spherical environment. ...
We now can reinterpret Algorithm 2 as a de Casteljau algorithm which uses different (spherical) barycentric coordinates for each sub-triangle T ( ) ij k instead of using the same barycentric coordinates ...
doi:10.1016/j.cam.2004.07.030
fatcat:ha4gvkmw55dpfk44j6vlh3yxqq
A Generic and Scalable Pipeline for GPU Tetrahedral Grid Rendering
2006
IEEE Transactions on Visualization and Computer Graphics
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At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local barycentric coordinates. ...
This ray is sampled on a spherical slice with distance zs from the eye point. The barycentric coordinate of the sample point is obtained by setting t as the depth of the actual spherical slice, zs. ...
First, for every element the matrix required to transform eye coordinates into local barycentric coordinates is computed. ...
doi:10.1109/tvcg.2006.110
pmid:17080871
fatcat:hj2qjmwwmrdoxpmlokuicf34sm
Fundamentals of spherical parameterization for 3D meshes
2003
ACM Transactions on Graphics
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We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection ...
Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity are not ...
Generalizing the barycentric coordinates theory to spherical embeddings is not straightforward. ...
doi:10.1145/882262.882276
fatcat:pamhzygwvvdo3mm3g7yj2slogu
Fundamentals of spherical parameterization for 3D meshes
2003
ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03
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We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection ...
Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity are not ...
Generalizing the barycentric coordinates theory to spherical embeddings is not straightforward. ...
doi:10.1145/1201775.882276
fatcat:6qllnqlobjc2zgr7sorwknwyxq
Generalized barycentric coordinates and applications
2015
Acta Numerica
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This paper surveys the construction, properties, and applications of generalized barycentric coordinates on polygons and polyhedra. ...
Spherical coordinates Spherical barycentric coordinates for points in a spherical triangle were studied by Möbius (1846, Sec. 14) and Alfeld, Neamtu and Schumaker (1996) , and used in the latter to ...
Unlike in the case of a planar triangle, spherical barycentric coordinates do not in general sum to 1. ...
doi:10.1017/s0962492914000129
fatcat:s53htignyjaofovbogwalrfbiq
Research on Goods and the Ship Interaction Based on ADAMS
2017
MATEC Web of Conferences
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Figure 2 . 2 Barycentric coordinates curve.
Figure 3 . 3 Barycentric coordinates curve.The rigid body under the constraint of barycentre trajectory is shown inFig. 4. ...
Get the change of barycentric coordinates as shown in
Table 1:
Table 1. ...
doi:10.1051/matecconf/20179511002
fatcat:ejoqfuwqgzfnncg5cmb25qbftq
The Celestial Reference System in Relativistic Framework
1990
Symposium - International astronomical union
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The concept of reference system, reference frame, coordinate system and celestial sphere in a relativistic framework are given. ...
The problems on the choice of celestial coordinate systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5. ...
It is neither stationary nor spherically symmetric. ...
doi:10.1017/s0074180900086435
fatcat:urb36bg5q5fghfxeqcoszwdc3i
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